
Title: Subset Symbol

Series: Advent of Mathematical Symbols

YouTubeTitle: Advent of Mathematical Symbols  Part 27  Subset Symbol

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Subtitle in English
1 00:00:00,600 –> 00:00:03,672 Hello and welcome back to the next mathematical symbol.
2 00:00:03,872 –> 00:00:05,840 Which is the subset symbol.
3 00:00:06,100 –> 00:00:11,043 For denoting such a subset relation you either see this symbol or that.
4 00:00:11,386 –> 00:00:19,822 Personally I prefer this notation, because the line here immediately tells you that the equality of sets is also allowed here.
5 00:00:20,414 –> 00:00:25,040 However some authors take this simple arc here. Maybe because it’s shorter.
6 00:00:25,414 –> 00:00:30,375 Therefore please always pay attention to which symbol is used in a given book.
7 00:00:30,886 –> 00:00:36,776 It’s very important, because often there is also a notation which is used to denote a proper subset.
8 00:00:37,400 –> 00:00:41,490 This means there the equality is actually not allowed.
9 00:00:41,843 –> 00:00:47,272 Hence if we use the first notation here, we can do the same if we denote inequalities.
10 00:00:47,886 –> 00:00:52,891 So you see, if we want to denote a proper subset, we can just omit the line here.
11 00:00:53,343 –> 00:00:58,999 So unfortunately this is the same symbol some people use to denote a general subset.
12 00:00:59,429 –> 00:01:05,141 However this also means that these people need another notation for a proper subset
13 00:01:05,341 –> 00:01:10,151 and usually they use the first symbol, where they just cross the line underneath.
14 00:01:10,571 –> 00:01:16,976 Ok, so in summary what you should remember is that the symbols here come always in these two combinations
15 00:01:17,343 –> 00:01:21,773 and they just tell you that one set is contained in another.
16 00:01:22,214 –> 00:01:27,271 So if this here is the set B, the set A should lie completely inside
17 00:01:27,657 –> 00:01:31,911 and then we would just write: “A is a subset of B”
18 00:01:32,414 –> 00:01:36,713 and indeed most of the time we will not exclude the equality here
19 00:01:37,343 –> 00:01:42,982 and now this symbol just means that for all x the following implication is true.
20 00:01:43,182 –> 00:01:47,143 So if x is an element in A, it’s also an element in B.
21 00:01:47,900 –> 00:01:52,572 So you see, this new definition just goes back to the element relation
22 00:01:52,772 –> 00:01:59,861 and now since we have the implication from left to right, you also often see a mirrored version of this symbol.
23 00:02:00,343 –> 00:02:04,341 More precisely you would say: “B is a superset of A”
24 00:02:04,743 –> 00:02:08,687 and then of course this means exactly the same thing written here.
25 00:02:08,887 –> 00:02:13,995 So I would say now you know the subset symbol and also the superset symbol
26 00:02:14,195 –> 00:02:20,959 and if you want to learn more details about sets, I have a whole video series about it called “start learning sets”.
27 00:02:21,243 –> 00:02:25,764 So I really hope I see you there or in the next video about mathematical symbols.
28 00:02:26,029 –> 00:02:28,552 So have a nice day and bye.